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Mean Value Theorem for Integrals

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First published at 07:03 UTC on December 21st, 2019.

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MES

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In this video I go over the Mean Value Theorem for Integrals which states that for any continuous function from x = a to x = b there exists a number c in that interval such that f(c) is equal to the average of the function during that interval. The theorem is a direct consequence of the original Mean Value Theorem which is for derivatives. This theorem also shows that in that interval the average value can be considered the height of a rectangle with the same area as that under the curve.

Download the notes in my video: http://1drv.ms/1JCnGP3

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/mean-value-theorem-for-integrals

Related Videos:

Mean Value Theorem - A Simple Proof: http://youtu.be/x-2MiiG2E38
Integrals and Average Value: Example 1: http://youtu.be/Ps1IPP4O_Lo
Integrals and Average Value of a Function: http://youtu.be/Xo2SSQOki1g
Integrals and Work: Introduction: http://youtu.be/dNmfGmWyMqc
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Fundamental Theorem of Calculus - Intro and Proof of Part 2 of the Theorem: http://youtu.be/yuIl-BPQHss
Fundamental Theorem of Calculus - Introduction and Part 1 of the Theorem: http://youtu.be/3o8Q6UJzJyk
Fundamental Theorem of Calculus - Proof of Part 1 of the Theorem: http://youtu.be/CAqTwiPxYwU .